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Optimisation in space of measures and optimal design

Ilya Molchanov, Sergei Zuyev (2010)

ESAIM: Probability and Statistics

The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation framework...

Optimising prediction error among completely monotone covariance sequences.

McVinish, Ross S. (2008)

Electronic Communications in Probability [electronic only]

Optimum stopping rules on the sequence of statistically dependent vectors

Jiří Cochlar (1980)

Kybernetika

Option price when the stock is a semimartingale.

Klebaner, Fima (2002)

Electronic Communications in Probability [electronic only]

Optional splitting formula in a progressively enlarged filtration

Shiqi Song (2014)

ESAIM: Probability and Statistics

Let $𝔽_{}^{}$ F be a filtration andτbe a random time. Let $𝔾_{}^{}$ G be the progressive enlargement of $𝔽_{}^{}$ F withτ. We study the following formula, called the optional splitting formula: For any $𝔾_{}^{}$ G-optional processY, there exists an $𝔽_{}^{}$ F-optional processY′ and a function Y′′ defined on [0,∞] × (ℝ+ × Ω) being $ℬ [0, \infty] \otimes 𝒪 (𝔽_{}^{})$ ℬ[0,∞]⊗x1d4aa;(F) measurable, such that $Y = Y^{'} 1_{[0, τ)}^{} + Y^{''} (τ) 1_{[τ, \infty)}^{} .$ Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random timesτ1,...,τk). We are interested in this formula because of its fundamental role in many...